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Topics in Harmonic Analysis and Ergodic Theory Joseph M. Rosenblatt, Alexander M. Stokolos, Ahmed I. Zayed ISBN: 0821842358 Paperback American Mathematical Society Usually despatched within 3 to 9 days

There are strong connections between harmonic analysis and ergodic theory. A recent example of this interaction is the proof of the spectacular result by Terence Tao and Ben Green that the set of prime numbers contains arbitrarily long arithmetic progressions. The breakthrough achieved by Tao and Green is attributed to applications of techniques from ergodic theory and harmonic analysis to problems in number theory.Articles in the present volume are based on talks delivered by plenary speakers at a conference on Harmonic Analysis and ergodic Theory (DePaul University, Chicago, December 2-4, 2005). Of ten articles, four are devoted to ergodic theory and six to harmonic analysis, although some may fall in either category. The articles are grouped in two parts arranged by topics. Among the topics are ergodic averages, central limit theorems for random walks, Borel foliations, ergodic theory and low pass filters, data fitting using smooth surfaces, Nehari's theorem for a polydisk, uniqueness theorems for multi-dimensional trigonometric series, and Bellman and s-functions.In addition to articles on current research topics in harmonic analysis and ergodic theory, this book contains survey articles on convergence problems in ergodic theory and uniqueness problems on multi-dimensional trigonometric series.

Ergodic Theory: with a view towards Number Theory, by Einsiedler and Ward Terry Tao's blog Akshay Venkatesh's lecture notes Ben Green's lecture notes

We now turn to several specific examples of this principle in various contexts.  We begin with the more “combinatorial” or “non-ergodic theoretical” instances of this principle, in which there is no underlying probability measure involved; these situations are simpler than the ergodic-theoretic ones, but already illustrate many of the key features of this principle in action.

Abstract. The paper study counter-dependent pseudorandom number generators based on m-variate (m> 1) ergodic mappings of the space of 2-adic integers Z2. The sequence of internal states of these generators is defined by the recurrence law xi+1 = H B i (xi) mod 2 n, whereas their output sequence is zi = F B i (xi) mod 2 n; here xj, zj are m-dimensional vectors over Z2. It is shown how the results obtained for a univariate case could be extended to a multivariate case. 1.

Foundations of Cryptography. Basic Tools. Cambridge Univ – Goldreich - 2001

129 Uniform distribution of sequences – Kuipers, Niederreiter - 1974

MATH 254A : Topics in Ergodic Theory Course description: Basic Ergodic theorems (pointwise, mean, maximal) and recurrence theorems (Poincare, Khintchine, etc.)  Topological dynamics.  Structural theory of measure-preserving systems; characteristic factors.  Spectral theory of dynamical systems.  Multiple recurrence theorems (Furstenberg, etc.) and connections with additive combinatorics (e.g. Szemerédi’s theorem).  Orbits in homogeneous spaces, especially nilmanifolds; Ratner’s theorem.  Further topics as time allows may include joinings, dynamical entropy, return times theorems, arithmetic progressions in primes, and/or

        Instructor: Terence Tao, tao@math.ucla.edu, x64844, MS 6183

Abstract  The pointwise ergodic theorem is proved for prime powers for functions inL p,p>1. This extends a result of Bourgain where he proved a similar theorem forp>(1+√3)/2.

I am hop

Many areas of active research within the broad field of number theory relate to properties of polynomials, and this volume displays the most recent and most interesting work on this theme. The 2006 Number Theory and Polynomials workshop in Bristol drew together international researchers with a variety of number-theoretic interests, and the book’s contents reflect the quality of the meeting. Topics covered include recent work on the Schur-Siegel-Smyth trace problem, Mahler measure and its generalisations, the merit factor problem, Barker sequences, K3-surfaces, self-inversive polynomials, Newman’s inequality, algorithms for sparse polynomials, the integer transfinite diameter, divisors of polynomials, non-linear recurrence sequences, polynomial ergodic averages, and the Hansen-Mullen primitivity conjecture. With surveys and expository articles presenting the latest research, this volume is essential for graduates and researchers looking for a snapshot of current progress in polynomials and number theory.• An invaluable resource to both students and experts in this area, with survey articles on the most important topics in the field • Expository articles introduce graduate students to some problems of active interest • The inclusion of new results from leading experts in the field provides a snapshot of current progress